Theorems · Theorem · group theory
Finset.sum_disjUnion
∀ {ι : Type u_1} {M : Type u_4} {s₁ s₂ : Finset ι} [inst : AddCommMonoid M] {f : ι → M} (h : Disjoint s₁ s₂),
∑ x ∈ s₁.disjUnion s₂ h, f x = ∑ x ∈ s₁, f x + ∑ x ∈ s₂, f x- Cited by
- 8 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement and proof · cited by 5,195
- zero_addproof · cited by 2,366
- Disjointstatement and proof · cited by 2,201
- Finset.disjUnionstatement and proof · cited by 55
- Finset.foldproof · cited by 46
- Finset.fold_disjUnionproof · cited by 2
Cited by8
Results whose statement or proof uses this declaration.
- Finset.sum_disjSumproof · cited by 7
- IsCompl.sum_add_sumproof · cited by 2
- QuadraticMap.map_sumproof · cited by 2
- Matrix.detp_mulproof · cited by 1
- MvPolynomial.mul_esymm_eq_sumproof · cited by 1
- QuadraticMap.map_sum'proof · cited by 1
- Matrix.det_eq_detp_sub_detpproof · cited by 0
- Finset.sum_sum_Ioi_add_eq_sum_sum_off_diagproof · cited by 0